The Helium Wave Equation

This paper is a sequel to the preceding one by Gronwall. In Part I it is shown that the ground state eigenfunction, if it exists, cannot have the form =p, k=0^s^p+a^p, k () cosk, where s=r^1{2}= (r₁^{_^2+r₂^_^2) }^1{2}, and is some constant. In Part II, it is assumed that the solution of Gronwall's infinite system of ordinary differential equations (see preceding abstract) is to be found by extrapolation from a finite system. Arguments are given to show that if the wave function is finite everywhere except at the origin, then the expansion about the origin is of the form =k=0^c^ (k) (s, , ) (logs) ^k, where the c^ (k) 's are ascending power series in s.